Optimal support positioning of a rectangular plate in a stability problem under temperature field exposure

Abstract

Introduction. Thin plates are widely used structural elements in modern civil, mechanical, aeronautical, and marine engineering design. Alongside the temperature field, the middle plain of plates is subjected to uniformly distributed normal mechanical forces, with σφ intensity, which raises the stability problem of thin plates. The strength and stability of rectangular plates have been investigated by S.P. Timoshenko [1], S.A. Ambartsumyan [2] and others. In the field of design of thin structure elements, the optimal positioning of plate supports has been studied in the works of V.Ts. Gnuni [3], M.V. Belubekyan [4], and A.V. Eloyan [5, 6]. However, the problem of optimal support positioning has not been sufficiently studied, particularly regarding the thermoelastic stability of thin plates. The simultaneous exposure of mechanical forces and temperature field on a rectangular plate poses the issue of an efficient parameter с that determines the positions of transverse supports along the length of a plate thus ensuring the maximum buckling load.
Aim. To calculate the optimal values of a parameter α = c/a in accordance with σ̅, h̅, values for different side ratios λ=a/b of a plate for specified temperature values.
Materials and methods. Elastic isotropic plates were used, the maximum buckling load was determined.
Results and conclusions. According to the results, the optimal location of plate supports for values λ = a/b–1/2,1 is determined by σ̅ = 3β depending on the plate temperature. The maximum buckling load is determined when σ̅ = 3β, h̅ = 0,01, w* = 1,772, α = 0,37, Т = 300 °С.